A numerical model for the axisymmetric equilibrium shape of drops in uniform motion: Effects of external flow, electric field and surface charge

In the past the best models of raindrop shapes were based on a perturbation form of Laplace's formula valid only for small amplitude distortion from the effect of an aerodynamic pressure around a sphere. In contrast, the current force balance model uses the complete form of differential Laplace's formula and includes adjustments to the aerodynamic pressure distribution for the effects of drop distortion and Reynolds number. The raindrop shapes under the influence of vertical electric fields and drop charges has also been investigated. A finite volume method with numerically generated transformation to a boundary-fitted coordinate system was used to calculate the shape-dependent electric field. Sufficient constraints (viz, drop volume, overall force balance, and shape-dependent surface distributions of aerodynamic and electrostatic stresses) allow the calculation of a unique shape by integration from the upper to lower pole of raindrop using a multiple iteration scheme.Based on the good agreement with wind tunnel observations, it appears that the model axis ratios from aerodynamic distortion provide the best approximation to date for raindrop size up to d = 9 mm. The model shapes closely fit the profiles of rather large raindrops (d = 5 mm). The model has been verified against solutions for a stationary drop in a uniform electric field (Taylor, 1964; Brazier-Smith, 1971; and Zrnic et al., 1984). Numerical shapes of falling drops in electric fields show a pronounced extension of the upper pole. The increased fall speed of electrostatically stretched drops enhances the aerodynamic flattening the base. The resultant triangular drop profiles are similar to wind tunnels observations (Richards and Dawson, 1971; and Rasmussen et al., 1985).U of I OnlyETDs are only available to UIUC Users without author permissio